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Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Educational Resource on Step Functions #### Image Description: The image contains a step function graph. The graph is a plot of \( f(x) = \lfloor x \rfloor \), which is the floor function. This function returns the greatest integer less than or equal to \( x \). #### Key Elements of the Graph: - **Axes**: The horizontal axis represents \( x \), and the vertical axis represents \( f(x) \). - **Graph Characteristics**: The graph consists of horizontal segments with closed circles on the left end and open circles on the right end, illustrating the value of the floor function at different integer points. #### Questions Based on the Graph: 1. **What is the \( y \) value when:** - \( \bullet \, x = -3 \) - b) \( x = 0 \) - c) \( x = 4 \) 2. **What is the domain and range of this function?** 3. **Determine if there is a minimum, maximum, and line of symmetry.** #### Detailed Explanation: 1. **Finding \( y \) values:** - For \( x = -3 \): - The floor function value at \( x = -3 \) is \( f(-3) = -3 \). - For \( x = 0 \): - The floor function value at \( x = 0 \) is \( f(0) = 0 \). - For \( x = 4 \): - The floor function value at \( x = 4 \) is \( f(4) = 4 \). 2. **Domain and Range:** - **Domain**: The domain of the floor function \( f(x) = \lfloor x \rfloor \) is all real numbers, \( (-\infty, +\infty) \). - **Range**: The range of this function is all integers, \( \mathbb{Z} \). 3. **Determining Minimum, Maximum, and Line of Symmetry:** - This function does **not** have a minimum or maximum value since it can take on any integer value from negative to positive infinity. - There is **no line of symmetry** in the traditional sense (global symmetry), but each step segment is horizontally symmetric where each individual step is symmetric about its midpoint. This step function graph provides a clear
Transcribed Image Text:### Educational Resource on Step Functions #### Image Description: The image contains a step function graph. The graph is a plot of \( f(x) = \lfloor x \rfloor \), which is the floor function. This function returns the greatest integer less than or equal to \( x \). #### Key Elements of the Graph: - **Axes**: The horizontal axis represents \( x \), and the vertical axis represents \( f(x) \). - **Graph Characteristics**: The graph consists of horizontal segments with closed circles on the left end and open circles on the right end, illustrating the value of the floor function at different integer points. #### Questions Based on the Graph: 1. **What is the \( y \) value when:** - \( \bullet \, x = -3 \) - b) \( x = 0 \) - c) \( x = 4 \) 2. **What is the domain and range of this function?** 3. **Determine if there is a minimum, maximum, and line of symmetry.** #### Detailed Explanation: 1. **Finding \( y \) values:** - For \( x = -3 \): - The floor function value at \( x = -3 \) is \( f(-3) = -3 \). - For \( x = 0 \): - The floor function value at \( x = 0 \) is \( f(0) = 0 \). - For \( x = 4 \): - The floor function value at \( x = 4 \) is \( f(4) = 4 \). 2. **Domain and Range:** - **Domain**: The domain of the floor function \( f(x) = \lfloor x \rfloor \) is all real numbers, \( (-\infty, +\infty) \). - **Range**: The range of this function is all integers, \( \mathbb{Z} \). 3. **Determining Minimum, Maximum, and Line of Symmetry:** - This function does **not** have a minimum or maximum value since it can take on any integer value from negative to positive infinity. - There is **no line of symmetry** in the traditional sense (global symmetry), but each step segment is horizontally symmetric where each individual step is symmetric about its midpoint. This step function graph provides a clear
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